Finite Group Databasebeta

← Group #313654

Character table — Group #313654

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888244444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-111111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111111-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1111-1-111-1-1-11
χ17222222222-22-22-22-2000000002222-2-200002222-2-2-2-200000000-2-200-2-2002200000000000000000000
χ18222222222-22-22-22-2000000002222-2-20000-2-2-2-2222200000000-2-2002200-2-200000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-20000000022002200-2-200000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-22222000000002200-2-2002200000000000000000000
χ2122222222-22-22-22-22222222220000-2-2-2-2-2-20000000000000000002200220000000000-200-200000000
χ2222222222-22-22-22-22222222220000-2-2-2-2-2-2000000000000000000-2-200-2-20000000000200200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-222220000000000000000002200-2-20000000000-200200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-22222000000000000000000-2-200220000000000200-200000000
χ25222-2-2-22-2020-20-2022222-2-2-2-20000000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2002i−2i002i−2i00000000000000002−22−200
χ26222-2-2-22-2020-20-2022222-2-2-2-20000000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200−2i2i00−2i2i0000000000000000−22−2200
χ27222-2-2-22-2020-20-2022222-2-2-2-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2002i−2i002i−2i0000000000000000−22−2200
χ28222-2-2-22-2020-20-2022222-2-2-2-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200−2i2i00−2i2i00000000000000002−22−200
χ29222-2-2-22-2020-20-202-2-2-2-222220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2002i−2i00−2i2i00000000000000002−2−2200
χ30222-2-2-22-2020-20-202-2-2-2-222220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200−2i2i002i−2i0000000000000000−222−200
χ31222-2-2-22-2020-20-202-2-2-2-222220000000000−i2−i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2002i−2i00−2i2i0000000000000000−222−200
χ32222-2-2-22-2020-20-202-2-2-2-222220000000000−i2−i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200−2i2i002i−2i00000000000000002−2−2200
χ3322-22-2-2-2220-20-2020i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00i2i2−i2−i22i−2i2i−2i000022−2−222−2−2000000002-2i2i2−i2−i222−2−2000000000000
χ3422-22-2-2-2220-20-2020i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00i2i2−i2−i2−2i2i−2i2i0000−2−222−2−22200000000-22−i2−i2i2i222−2−2000000000000
χ3522-22-2-2-2220-20-2020i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i00i2i2−i2−i22i−2i2i−2i000022−2−222−2−200000000-22−i2−i2i2i2−2−222000000000000
χ3622-22-2-2-2220-20-2020i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i00i2i2−i2−i2−2i2i−2i2i0000−2−222−2−222000000002-2i2i2−i2−i2−2−222000000000000
χ3722-22-2-2-2220-20-2020−i2−i2i2i2−i2−i2i2i22i2i−2i−2i00−i2−i2i2i22i−2i2i−2i0000−2−222−2−222000000002-2−i2−i2i2i2−2−222000000000000
χ3822-22-2-2-2220-20-2020−i2−i2i2i2−i2−i2i2i22i2i−2i−2i00−i2−i2i2i2−2i2i−2i2i000022−2−222−2−200000000-22i2i2−i2−i2−2−222000000000000
χ3922-22-2-2-2220-20-2020−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00−i2−i2i2i22i−2i2i−2i0000−2−222−2−22200000000-22i2i2−i2−i222−2−2000000000000
χ4022-22-2-2-2220-20-2020−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00−i2−i2i2i2−2i2i−2i2i000022−2−222−2−2000000002-2−i2−i2i2i222−2−2000000000000
χ412-222-22-2-222-2-222-2-22i−2i2i−2i2i−2i2i−2i2-22-2-222i−2i2i−2i00000000000000002-20000000000002i−2i2i−2i000000000000
χ422-222-22-2-222-2-222-2-22i−2i2i−2i2i−2i2i−2i-22-22-222i−2i2i−2i0000000000000000-22000000000000−2i2i−2i2i000000000000
χ432-222-22-2-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i2-22-2-22−2i2i−2i2i00000000000000002-2000000000000−2i2i−2i2i000000000000
χ442-222-22-2-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i-22-22-22−2i2i−2i2i0000000000000000-220000000000002i−2i2i−2i000000000000
χ452-222-22-2-22-2-222-2-22000000002-22-22-20000000000002i−2i2i−2i2i−2i2i−2i-22000000002i−2i2i−2i0000000000000000
χ462-222-22-2-22-2-222-2-22000000002-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i-2200000000−2i2i−2i2i0000000000000000
χ472-222-22-2-22-2-222-2-2200000000-22-222-20000000000002i−2i2i−2i2i−2i2i−2i2-200000000−2i2i−2i2i0000000000000000
χ482-222-22-2-22-2-222-2-2200000000-22-222-2000000000000−2i2i−2i2i−2i2i−2i2i2-2000000002i−2i2i−2i0000000000000000
χ492-222-22-2-2-222-2-222-22i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i000000000000000000000000000000000002-202i−2i000000
χ502-222-22-2-2-222-2-222-22i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i00000000000000000000000000000000000-220−2i2i000000
χ512-222-22-2-2-222-2-222-2−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i000000000000000000000000000000000002-20−2i2i000000
χ522-222-22-2-2-222-2-222-2−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i00000000000000000000000000000000000-2202i−2i000000
χ532-2-222-22-22020-20-202−2−222−2−222i−2i−2i2i002−2−2200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i200002-20000−222−2−i2i2i2−i2000000000000
χ542-2-222-22-22020-20-202−2−222−2−222i−2i−2i2i002−2−220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000-2200002−2−22−i2i2i2−i2000000000000
χ552-2-222-22-22020-20-202−2−222−2−22−2i2i2i−2i002−2−2200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000-2200002−2−22i2−i2−i2i2000000000000
χ562-2-222-22-22020-20-202−2−222−2−22−2i2i2i−2i002−2−220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i200002-20000−222−2i2−i2−i2i2000000000000
χ572-2-222-22-22020-20-20−222−2−222−22i−2i−2i2i00−222−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i200002-200002−2−22i2−i2−i2i2000000000000
χ582-2-222-22-22020-20-20−222−2−222−22i−2i−2i2i00−222−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000-220000−222−2i2−i2−i2i2000000000000
χ592-2-222-22-22020-20-20−222−2−222−2−2i2i2i−2i00−222−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000-220000−222−2−i2i2i2−i2000000000000
χ602-2-222-22-22020-20-20−222−2−222−2−2i2i2i−2i00−222−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i200002-200002−2−22−i2i2i2−i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-4-44-40-404040-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ63444-4-4-44-40-404040-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6444-44-4-4-44-404040-402i22i2−2i2−2i22i22i2−2i2−2i2000000−2i2−2i22i22i20000000000000000000000000000000000000000000000
χ6544-44-4-4-44-404040-40−2i2−2i22i22i2−2i2−2i22i22i20000002i22i2−2i2−2i20000000000000000000000000000000000000000000000
χ6644-4-444-4-4000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000022−22−22220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-444-4-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000−222222−2200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-444-4-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000000022−22−222200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6944-4-444-4-400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000−222222−220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ704-444-44-4-4-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ714-44-44-4-4404040-40-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ724-44-44-4-4404040-40-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ734-44-44-4-440-40-404040000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ744-44-44-4-440-40-4040400000000000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ754-4-444-44-4-40-40404022−22−222222−22−2222000000−222222−220000000000000000000000000000000000000000000000
χ764-4-444-44-4-40-404040−222222−22−222222−2200000022−22−22220000000000000000000000000000000000000000000000
χ774-4-4-4-44440000000022−22−2222−222222−220000000000000022−22−22222-2-22-222-2000000000000000000000000000000
χ784-4-4-4-44440000000022−22−2222−222222−2200000000000000−222222−22-222-22-2-22000000000000000000000000000000
χ794-4-4-4-444400000000−222222−2222−22−22220000000000000022−22−2222-222-22-2-22000000000000000000000000000000
χ804-4-4-4-444400000000−222222−2222−22−222200000000000000−222222−222-2-22-222-2000000000000000000000000000000

Here i is the imaginary unit (i² = −1).